So the closest thing to a "Boss Theme" in Ace Attorney is the ~allegro~ version of the Cross Examination theme, when it gets all intense, usually because you're finally cross examining the actual murderer and have them on the ropes. And Dai Gyakuten Saiban (the unlocalized Sherlock Holmes crossover) has by far the best one in the series, because it has the best musical and artistic direction in the series, because it's a spiritual successor to PLvAA:

I don't even know where to begin. There too many really, really good boss themes that I enjoy. I don't have the time to go through them all right now so I'm just going to start with "He of the Name" from Bravely Default:

NieR: Automata has one of those dangerous OSTs where I'll end up listening to almost the entire thing if I go looking for any part of it. I've already changed which track I'm posting three times, so I'm just going to stop now and say that it could easily have been any other boss theme. They're all amazing.

I could probably pick any of the boss themes from Shovel Knight, but since this one is based off of my favorite level theme, I had to pick it. The Black Knight fight in the Tower of Fate was also a close consideration.